Trick question. If we're talking the 14th century Black Death (1346-53), the question arises, who would do the invading? One's own country, if one is European, would already be depopulated, with the heart breaking but economically stimulating effects that would have. The Muslim Middle East was in no shape to take advantage of the situation even if they had wanted to, those Middle Easterners having also suffered from this Central Asian import, with devastating results. (It also did a number on India and China) Ibn al-Wardi (d. 1349 of plague) of Syria gives an eye-witness account that doesn't differ much from what you would find in European writings.

If you're interested in the ME side of things, you might check out Michael Dols's book The Black Death in the Middle East. A shorter piece ( THE COMPARATIVE COMMUNAL RESPONSES TO THE BLACK DEATH IN MUSLIM AND CHRISTIAN SOCIETIES) by the same author can be found here